I would not use solid oak for the carcass of the cage. Oak is a great wood but notorious for expansion and contraction. Not good for a reptile enclosure which will likely experience temperature differentials inside and outside.
Instead I would use oak laminated plywood for the carcass of the cage and use solid oak for the face frame. You might spend some time trying to find a plywood supplier that can match the species and cut of the oak you have access to.
For a finish you want to pay particular attention to the floor and first several inches of the cage walls. That is where most of the damage from urates, water spills, etc. will occur. Recently on this forum there has been a shift towards using a plastic floor of some sort. Vinyl film, linoleum, expanded PVC sign board, fiberglass reinforced panel are all recommended. Of those linoleum and other vinyl floors are often the easiest to find. Since many of them come in attractive patterns and colors people have even used them to line the walls of the cage, often giving a very nice look combined with a real-wood exterior.
If you want a stained/clear coated wood look on the inside I would still use plastic flooring of some sort on the bottom and first several inches of the cage walls. The rest can be clear coated with a water-based finish. Oil-based polyurethanes have very long offgass times and are not recommended for use on the interiors of cabinets. One poster on this forum has cages he built over a year ago still releasing toxic smelling fumes. Needless to say they sit empty.
-----
Current snakes:
0.0.1 Gonyosoma oxycephala - Java locale (green)
1.2 Gonyosoma oxycephala - Jave local (green)
2.2 Gonyosoma janseni - Seleyar locale (all black)
1.2 Gonyosoma janseni - Celebes locale (Black & Tan)